It sounds as if your reverse gearing may be slipping, though, it is slipping under lots of stress. Reverse is normally a high-stress business as the tranny drops down, uses a pretty much direct 1:1 linkage so that when it pulls, it pulls at your engine’s full capacity. So, when you put the truck into gear on a hill not only are you asking the transmission to pull strongly and directly to the rear, but you are also adding the inertia caused by the incline. The transmission has to overcome that inertia first before it even begins pulling.
With that said, if your transmission’s reverse is beginning to wear out, the it will shift in sharply and try to slip out but it will not succeed. Therefore, you have juddering. The problem may lie in the gearing itself, though, I do not think that is the primary issue.
I think your transmission’s primary issue is in either the clutches or the bands and clutches. As I just said, when your transmission goes into reverse, it is pretty much a 1:1 lockup between the rear wheels and the engine. In order to handle this, you are asking the clutches to handle a full torque load when they may not be willing to do so. If they are worn, then the clutches will allow the slippage. This situation is compounded by the bands contributing to the problem.
What this means is that you will have to have the bands and clutches replaced. In order to do this, your transmission will have to be stripped down to just about the last nut and bolt. So, here’s what I would suggest you do, ask your transmission shop to find a replacement transmission. You may be lucky and they may be able to find a transmission replacement from a partially junked vehicle. The body and/or the engine may be shot, but the transmission may be in good shape and may last for many miles.
Indeed, this is the less expensive option of the three available to you as it is likely you will only have to pay the cartage from the scrapyard, a small fee for the transmission and the fee for having it pulled out. The other options, a rebuilt transmission and replacing the bands/clutches/gears, are far more expensive. I honestly don’t know what the pricing may be in the U.K., where you are obviously writing from, but I suspect it may be similar to the pricing in the states so that the more expensive options are still more expensive.
Whatever the expense, though, your transmission needs work. I would have it done as soon as possible.
Please let me know what your shop finds as I honestly like to know what happens.